{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    # Check if notebook is running in Google Colab\n",
    "    import google.colab\n",
    "    # Get additional files from Github\n",
    "    !wget https://raw.githubusercontent.com/krasserm/bayesian-machine-learning/dev/gaussian-processes/gaussian_processes_util.py\n",
    "    # Install additional dependencies\n",
    "    !pip install GPy==1.9.8\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian processes\n",
    "\n",
    "## Introduction\n",
    "\n",
    "In supervised learning, we often use parametric models $p(\\mathbf{y} \\lvert \\mathbf{X},\\boldsymbol\\theta)$ to explain data and infer optimal values of parameter $\\boldsymbol\\theta$ via [maximum likelihood](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation) or [maximum a posteriori](https://de.wikipedia.org/wiki/Maximum_a_posteriori) estimation. If needed we can also infer a full [posterior distribution](https://en.wikipedia.org/wiki/Posterior_probability) $p(\\boldsymbol\\theta \\lvert \\mathbf{X},\\mathbf{y})$ instead of a point estimate $\\boldsymbol{\\hat\\theta}$. With increasing data complexity, models with a higher number of parameters are usually needed to explain data reasonably well. Methods that use models with a fixed number of parameters are called parametric methods. \n",
    "\n",
    "In non-parametric methods, on the other hand, the number of parameters depend on the dataset size. For example, in [Nadaraya-Watson kernel regression](https://en.wikipedia.org/wiki/Kernel_regression), a weight $w_i$ is assigned to each observed target $y_i$ and for predicting the target value at a new point $\\mathbf{x}$ a weighted average is computed: \n",
    "\n",
    "$$f(\\mathbf{x}) = \\sum_{i=1}^{N}w_i(\\mathbf{x})y_i$$\n",
    "\n",
    "$$w_i(\\mathbf{x}) = \\frac{\\kappa(\\mathbf{x}, \\mathbf{x}_{i})}{\\sum_{i'=1}^{N}\\kappa(\\mathbf{x}, \\mathbf{x}_{i'})}$$\n",
    "\n",
    "Observations that are closer to $\\mathbf{x}$ have a higher weight than observations that are further away. Weights are computed from $\\mathbf{x}$ and observed $\\mathbf{x}_i$ with a kernel $\\kappa$. A special case is k-nearest neighbors (KNN) where the $k$ closest observations have a weight $1/k$, and all others have weight $0$. Non-parametric methods often need to process all training data for prediction and are therefore slower at inference time than parametric methods. On the other hand, training is usually faster as non-parametric models only need to remember training data. \n",
    "\n",
    "Another example of non-parametric methods are [Gaussian processes](https://en.wikipedia.org/wiki/Gaussian_process) (GPs). Instead of inferring a distribution over the parameters of a parametric function Gaussian processes can be used to infer a distribution over functions directly. A Gaussian process defines a prior over functions. After having observed some function values it can be converted into a posterior over functions. Inference of continuous function values in this context is known as GP regression but GPs can also be used for [classification](https://nbviewer.jupyter.org/github/krasserm/bayesian-machine-learning/blob/dev/gaussian-processes/gaussian_processes_classification.ipynb). \n",
    "\n",
    "A Gaussian process is a [random process](https://en.wikipedia.org/wiki/Stochastic_process) where any point $\\mathbf{x} \\in \\mathbb{R}^d$ is assigned a random variable $f(\\mathbf{x})$ and where the joint distribution of a finite number of these variables $p(f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$ is itself Gaussian:\n",
    "\n",
    "$$p(\\mathbf{f} \\lvert \\mathbf{X}) = \\mathcal{N}(\\mathbf{f} \\lvert \\boldsymbol\\mu, \\mathbf{K})\\tag{1}\\label{eq1}$$\n",
    "\n",
    "In Equation $(1)$, $\\mathbf{f} = (f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$, $\\boldsymbol\\mu = (m(\\mathbf{x}_1),...,m(\\mathbf{x}_N))$ and $K_{ij} = \\kappa(\\mathbf{x}_i,\\mathbf{x}_j)$. $m$ is the mean function and it is common to use $m(\\mathbf{x}) = 0$ as GPs are flexible enough to model the mean arbitrarily well. $\\kappa$ is a positive definite *kernel function* or *covariance function*. Thus, a Gaussian process is a distribution over functions whose shape (smoothness, ...) is defined by $\\mathbf{K}$. If points $\\mathbf{x}_i$ and $\\mathbf{x}_j$ are considered to be similar by the kernel the function values at these points, $f(\\mathbf{x}_i)$ and $f(\\mathbf{x}_j)$, can be expected to be similar too. \n",
    "\n",
    "Given a training dataset with noise-free function values $\\mathbf{f}$ at inputs $\\mathbf{X}$, a GP prior can be converted into a GP posterior $p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{X},\\mathbf{f})$ which can then be used to make predictions $\\mathbf{f}_*$ at new inputs $\\mathbf{X}_*$. By definition of a GP, the joint distribution of observed values $\\mathbf{f}$ and predictions $\\mathbf{f}_*$ is again a Gaussian which can be partitioned into\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}\\mathbf{f} \\\\ \\mathbf{f}_*\\end{pmatrix} \\sim \\mathcal{N}\n",
    "\\left(\\boldsymbol{0},\n",
    "\\begin{pmatrix}\\mathbf{K} & \\mathbf{K}_* \\\\ \\mathbf{K}_*^T & \\mathbf{K}_{**}\\end{pmatrix}\n",
    "\\right)\\tag{2}\\label{eq2}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{K}_* = \\kappa(\\mathbf{X},\\mathbf{X}_*)$ and $\\mathbf{K}_{**} = \\kappa(\\mathbf{X}_*,\\mathbf{X}_*)$. With $N$ training data and $N_*$ new input data $\\mathbf{K}$ is a $N \\times N$ matrix, $\\mathbf{K}_*$ a $N \\times N_*$ matrix and $\\mathbf{K}_{**}$ a $N_* \\times N_*$ matrix. Using standard rules for conditioning Gaussians, the predictive distribution is given by \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{X},\\mathbf{f}) &= \\mathcal{N}(\\mathbf{f}_* \\lvert \\boldsymbol{\\mu}_*, \\boldsymbol{\\Sigma}_*)\\tag{3}\\label{eq3} \\\\\n",
    "\\boldsymbol{\\mu_*} &= \\mathbf{K}_*^T \\mathbf{K}^{-1} \\mathbf{f}\\tag{4}\\label{eq4} \\\\\n",
    "\\boldsymbol{\\Sigma_*} &= \\mathbf{K}_{**} - \\mathbf{K}_*^T \\mathbf{K}^{-1} \\mathbf{K}_*\\tag{5}\\label{eq5}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "If we have a training dataset with noisy function values $\\mathbf{y} = \\mathbf{f} + \\boldsymbol\\epsilon$ where noise $\\boldsymbol\\epsilon \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_y^2 \\mathbf{I})$ is independently added to each observation then the predictive distribution is given by\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "p(\\mathbf{f}_* \\lvert \\mathbf{X}_*,\\mathbf{X},\\mathbf{y}) &= \\mathcal{N}(\\mathbf{f}_* \\lvert \\boldsymbol{\\mu}_*, \\boldsymbol{\\Sigma}_*)\\tag{6}\\label{eq6} \\\\\n",
    "\\boldsymbol{\\mu_*} &= \\mathbf{K}_*^T \\mathbf{K}_y^{-1} \\mathbf{y}\\tag{7}\\label{eq7} \\\\\n",
    "\\boldsymbol{\\Sigma_*} &= \\mathbf{K}_{**} - \\mathbf{K}_*^T \\mathbf{K}_y^{-1} \\mathbf{K}_*\\tag{8}\\label{eq8}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{K}_y = \\mathbf{K} + \\sigma_y^2\\mathbf{I}$. Although Equation $(6)$ covers noise in training data, it is still a distribution over noise-free predictions $\\mathbf{f}_*$. To additionally include noise $\\boldsymbol\\epsilon$ into predictions $\\mathbf{y}_*$ we have to add $\\sigma_y^2$ to the diagonal of $\\boldsymbol{\\Sigma_*}$\n",
    "\n",
    "$$\n",
    "p(\\mathbf{y}_* \\lvert \\mathbf{X}_*,\\mathbf{X},\\mathbf{y}) = \\mathcal{N}(\\mathbf{y}_* \\lvert \\boldsymbol{\\mu}_*, \\boldsymbol{\\Sigma}_* + \\sigma_y^2\\mathbf{I})\\tag{9}\\label{eq9}\n",
    "$$\n",
    "\n",
    "using the definitions of $\\boldsymbol{\\mu}_*$ and $\\boldsymbol{\\Sigma}_*$ from Equations $(7)$ and $(8)$, respectively. This is the minimum we need to know for implementing Gaussian processes and applying them to regression problems. For further details, please consult the literature in the [References](#References) section. The next section shows how to implement GPs with plain NumPy from scratch, later sections demonstrate how to use GP implementations from [scikit-learn](http://scikit-learn.org/stable/) and [GPy](http://sheffieldml.github.io/GPy/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation with NumPy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we will use the squared exponential kernel, also known as Gaussian kernel or RBF kernel:\n",
    "\n",
    "$$\n",
    "\\kappa(\\mathbf{x}_i,\\mathbf{x}_j) = \\sigma_f^2 \\exp\\left(-\\frac{1}{2l^2}\n",
    "  (\\mathbf{x}_i - \\mathbf{x}_j)^T\n",
    "  (\\mathbf{x}_i - \\mathbf{x}_j)\\right)\\tag{10}\n",
    "$$\n",
    "\n",
    "The length parameter $l$ controls the smoothness of the function and $\\sigma_f$ the vertical variation. For simplicity, we use the same length parameter $l$ for all input dimensions (isotropic kernel). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def kernel(X1, X2, l=1.0, sigma_f=1.0):\n",
    "    \"\"\"\n",
    "    Isotropic squared exponential kernel.\n",
    "    \n",
    "    Args:\n",
    "        X1: Array of m points (m x d).\n",
    "        X2: Array of n points (n x d).\n",
    "\n",
    "    Returns:\n",
    "        (m x n) matrix.\n",
    "    \"\"\"\n",
    "    sqdist = np.sum(X1**2, 1).reshape(-1, 1) + np.sum(X2**2, 1) - 2 * np.dot(X1, X2.T)\n",
    "    return sigma_f**2 * np.exp(-0.5 / l**2 * sqdist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other kernels that can be used for Gaussian processes. See \\[3\\] for a detailed reference or the scikit-learn documentation for [some examples](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prior\n",
    "\n",
    "Let's first define a prior over functions with mean zero and a covariance matrix computed with kernel parameters $l=1$ and $\\sigma_f=1$. To draw random functions from that GP we draw random samples from the corresponding multivariate normal. The following example draws three random samples and plots it together with the zero mean and the *uncertainty region* (the 95% highest density interval computed from the diagonal of the covariance matrix)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from gaussian_processes_util import plot_gp\n",
    "\n",
    "# Finite number of points\n",
    "X = np.arange(-5, 5, 0.2).reshape(-1, 1)\n",
    "\n",
    "# Mean and covariance of the prior\n",
    "mu = np.zeros(X.shape)\n",
    "cov = kernel(X, X)\n",
    "\n",
    "# Draw three samples from the prior\n",
    "samples = np.random.multivariate_normal(mu.ravel(), cov, 3)\n",
    "\n",
    "# Plot GP mean, uncertainty region and samples \n",
    "plot_gp(mu, cov, X, samples=samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `plot_gp` function is defined [here](gaussian_processes_util.py).\n",
    "\n",
    "### Prediction from noise-free training data\n",
    "\n",
    "To compute the sufficient statistics i.e. mean and covariance of the posterior we implement Equations $(7)$ and $(8)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.linalg import inv\n",
    "\n",
    "def posterior(X_s, X_train, Y_train, l=1.0, sigma_f=1.0, sigma_y=1e-8):\n",
    "    \"\"\"\n",
    "    Computes the suffifient statistics of the posterior distribution \n",
    "    from m training data X_train and Y_train and n new inputs X_s.\n",
    "    \n",
    "    Args:\n",
    "        X_s: New input locations (n x d).\n",
    "        X_train: Training locations (m x d).\n",
    "        Y_train: Training targets (m x 1).\n",
    "        l: Kernel length parameter.\n",
    "        sigma_f: Kernel vertical variation parameter.\n",
    "        sigma_y: Noise parameter.\n",
    "    \n",
    "    Returns:\n",
    "        Posterior mean vector (n x d) and covariance matrix (n x n).\n",
    "    \"\"\"\n",
    "    K = kernel(X_train, X_train, l, sigma_f) + sigma_y**2 * np.eye(len(X_train))\n",
    "    K_s = kernel(X_train, X_s, l, sigma_f)\n",
    "    K_ss = kernel(X_s, X_s, l, sigma_f) + 1e-8 * np.eye(len(X_s))\n",
    "    K_inv = inv(K)\n",
    "    \n",
    "    # Equation (7)\n",
    "    mu_s = K_s.T.dot(K_inv).dot(Y_train)\n",
    "\n",
    "    # Equation (8)\n",
    "    cov_s = K_ss - K_s.T.dot(K_inv).dot(K_s)\n",
    "    \n",
    "    return mu_s, cov_s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and apply them to noise-free training data `X_train` and `Y_train`. The following example draws three samples from the posterior and plots them along with the mean, uncertainty region and training data. In a noise-free model, variance at the training points is zero and all random functions drawn from the posterior go through the trainig points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Noise free training data\n",
    "X_train = np.array([-4, -3, -2, -1, 1]).reshape(-1, 1)\n",
    "Y_train = np.sin(X_train)\n",
    "\n",
    "# Compute mean and covariance of the posterior distribution\n",
    "mu_s, cov_s = posterior(X, X_train, Y_train)\n",
    "\n",
    "samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction from noisy training data\n",
    "\n",
    "If some noise is included in the model, training points are only approximated and the variance at the training points is non-zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "noise = 0.4\n",
    "\n",
    "# Noisy training data\n",
    "X_train = np.arange(-3, 4, 1).reshape(-1, 1)\n",
    "Y_train = np.sin(X_train) + noise * np.random.randn(*X_train.shape)\n",
    "\n",
    "# Compute mean and covariance of the posterior distribution\n",
    "mu_s, cov_s = posterior(X, X_train, Y_train, sigma_y=noise)\n",
    "\n",
    "samples = np.random.multivariate_normal(mu_s.ravel(), cov_s, 3)\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train, samples=samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of kernel parameters and noise parameter\n",
    "\n",
    "The following example shows the effect of kernel parameters $l$ and $\\sigma_f$ as well as the noise parameter $\\sigma_y$. Higher $l$ values lead to smoother functions and therefore to coarser approximations of the training data. Lower $l$ values make functions more wiggly with wide uncertainty regions between training data points. $\\sigma_f$ controls the vertical variation of functions drawn from the GP. This can be seen by the wide uncertainty regions outside the training data region in the right figure of the second row. $\\sigma_y$ represents the amount of noise in the training data. Higher $\\sigma_y$ values make more coarse approximations which avoids overfitting to noisy data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "params = [\n",
    "    (0.3, 1.0, 0.2),\n",
    "    (3.0, 1.0, 0.2),\n",
    "    (1.0, 0.3, 0.2),\n",
    "    (1.0, 3.0, 0.2),\n",
    "    (1.0, 1.0, 0.05),\n",
    "    (1.0, 1.0, 1.5),\n",
    "]\n",
    "\n",
    "plt.figure(figsize=(12, 5))\n",
    "\n",
    "for i, (l, sigma_f, sigma_y) in enumerate(params):\n",
    "    mu_s, cov_s = posterior(X, X_train, Y_train, l=l, \n",
    "                            sigma_f=sigma_f, \n",
    "                            sigma_y=sigma_y)\n",
    "    plt.subplot(3, 2, i + 1)\n",
    "    plt.subplots_adjust(top=2)\n",
    "    plt.title(f'l = {l}, sigma_f = {sigma_f}, sigma_y = {sigma_y}')\n",
    "    plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimal values for these parameters can be estimated by maximizing the log marginal likelihood which is given by<sup>[1][3]</sup>\n",
    "\n",
    "$$\n",
    "\\log p(\\mathbf{y} \\lvert \\mathbf{X}) = \n",
    "\\log \\mathcal{N}(\\mathbf{y} \\lvert \\boldsymbol{0},\\mathbf{K}_y) =\n",
    "-\\frac{1}{2} \\mathbf{y}^T \\mathbf{K}_y^{-1} \\mathbf{y} \n",
    "-\\frac{1}{2} \\log \\begin{vmatrix}\\mathbf{K}_y\\end{vmatrix} \n",
    "-\\frac{N}{2} \\log(2\\pi) \\tag{11}\n",
    "$$\n",
    "\n",
    "In the following we will minimize the negative log marginal likelihood w.r.t. parameters $l$ and $\\sigma_f$, $\\sigma_y$ is set to the known noise level of the data. If the noise level is unknown, $\\sigma_y$ can be estimated as well along with the other parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.linalg import cholesky, det\n",
    "from scipy.linalg import solve_triangular\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "def nll_fn(X_train, Y_train, noise, naive=True):\n",
    "    \"\"\"\n",
    "    Returns a function that computes the negative log marginal\n",
    "    likelihood for training data X_train and Y_train and given\n",
    "    noise level.\n",
    "\n",
    "    Args:\n",
    "        X_train: training locations (m x d).\n",
    "        Y_train: training targets (m x 1).\n",
    "        noise: known noise level of Y_train.\n",
    "        naive: if True use a naive implementation of Eq. (11), if\n",
    "               False use a numerically more stable implementation.\n",
    "\n",
    "    Returns:\n",
    "        Minimization objective.\n",
    "    \"\"\"\n",
    "    \n",
    "    Y_train = Y_train.ravel()\n",
    "    \n",
    "    def nll_naive(theta):\n",
    "        # Naive implementation of Eq. (11). Works well for the examples \n",
    "        # in this article but is numerically less stable compared to \n",
    "        # the implementation in nll_stable below.\n",
    "        K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \\\n",
    "            noise**2 * np.eye(len(X_train))\n",
    "        return 0.5 * np.log(det(K)) + \\\n",
    "               0.5 * Y_train.dot(inv(K).dot(Y_train)) + \\\n",
    "               0.5 * len(X_train) * np.log(2*np.pi)\n",
    "        \n",
    "    def nll_stable(theta):\n",
    "        # Numerically more stable implementation of Eq. (11) as described\n",
    "        # in http://www.gaussianprocess.org/gpml/chapters/RW2.pdf, Section\n",
    "        # 2.2, Algorithm 2.1.\n",
    "        \n",
    "        K = kernel(X_train, X_train, l=theta[0], sigma_f=theta[1]) + \\\n",
    "            noise**2 * np.eye(len(X_train))\n",
    "        L = cholesky(K)\n",
    "        \n",
    "        S1 = solve_triangular(L, Y_train, lower=True)\n",
    "        S2 = solve_triangular(L.T, S1, lower=False)\n",
    "        \n",
    "        return np.sum(np.log(np.diagonal(L))) + \\\n",
    "               0.5 * Y_train.dot(S2) + \\\n",
    "               0.5 * len(X_train) * np.log(2*np.pi)\n",
    "\n",
    "    if naive:\n",
    "        return nll_naive\n",
    "    else:\n",
    "        return nll_stable\n",
    "\n",
    "# Minimize the negative log-likelihood w.r.t. parameters l and sigma_f.\n",
    "# We should actually run the minimization several times with different\n",
    "# initializations to avoid local minima but this is skipped here for\n",
    "# simplicity.\n",
    "res = minimize(nll_fn(X_train, Y_train, noise), [1, 1], \n",
    "               bounds=((1e-5, None), (1e-5, None)),\n",
    "               method='L-BFGS-B')\n",
    "\n",
    "# Store the optimization results in global variables so that we can\n",
    "# compare it later with the results from other implementations.\n",
    "l_opt, sigma_f_opt = res.x\n",
    "\n",
    "# Compute posterior mean and covariance with optimized kernel parameters and plot the results\n",
    "mu_s, cov_s = posterior(X, X_train, Y_train, l=l_opt, sigma_f=sigma_f_opt, sigma_y=noise)\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With optimized kernel parameters, training data are reasonably covered by the 95% highest density interval and the mean of the posterior is a good approximation.\n",
    "\n",
    "### Higher dimensions\n",
    "\n",
    "The above implementation can also be used for higher input data dimensions. Here, a GP is used to fit noisy samples from a sine wave originating at $\\boldsymbol{0}$ and expanding in the x-y plane. The following plots show the noisy samples and the posterior mean before and after kernel parameter optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from gaussian_processes_util import plot_gp_2D\n",
    "\n",
    "noise_2D = 0.1\n",
    "\n",
    "rx, ry = np.arange(-5, 5, 0.3), np.arange(-5, 5, 0.3)\n",
    "gx, gy = np.meshgrid(rx, rx)\n",
    "\n",
    "X_2D = np.c_[gx.ravel(), gy.ravel()]\n",
    "\n",
    "X_2D_train = np.random.uniform(-4, 4, (100, 2))\n",
    "Y_2D_train = np.sin(0.5 * np.linalg.norm(X_2D_train, axis=1)) + \\\n",
    "             noise_2D * np.random.randn(len(X_2D_train))\n",
    "\n",
    "plt.figure(figsize=(14,7))\n",
    "\n",
    "mu_s, _ = posterior(X_2D, X_2D_train, Y_2D_train, sigma_y=noise_2D)\n",
    "plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train, \n",
    "           f'Before parameter optimization: l={1.00} sigma_f={1.00}', 1)\n",
    "\n",
    "res = minimize(nll_fn(X_2D_train, Y_2D_train, noise_2D), [1, 1], \n",
    "               bounds=((1e-5, None), (1e-5, None)),\n",
    "               method='L-BFGS-B')\n",
    "\n",
    "mu_s, _ = posterior(X_2D, X_2D_train, Y_2D_train, *res.x, sigma_y=noise_2D)\n",
    "plot_gp_2D(gx, gy, mu_s, X_2D_train, Y_2D_train,\n",
    "           f'After parameter optimization: l={res.x[0]:.2f} sigma_f={res.x[1]:.2f}', 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how the true sine wave is approximated much better after parameter optimization.\n",
    "\n",
    "## Libraries that implement GPs\n",
    "\n",
    "This section shows two examples of libraries that provide implementations of GPs. I'll provide only a minimal setup here, just enough for reproducing the above results. For further details please consult the documentation of these libraries.\n",
    "\n",
    "### Scikit-learn\n",
    "\n",
    "Scikit-learn provides a `GaussianProcessRegressor` for implementing [GP regression models](http://scikit-learn.org/stable/modules/gaussian_process.html#gaussian-process-regression-gpr). It can be configured with [pre-defined kernels and user-defined kernels](http://scikit-learn.org/stable/modules/gaussian_process.html#gp-kernels). Kernels can also be composed. The squared exponential kernel is the `RBF` kernel in scikit-learn. The `RBF` kernel only has a `length_scale` parameter which corresponds to the $l$ parameter above. To have a $\\sigma_f$ parameter as well, we have to compose the `RBF` kernel with a `ConstantKernel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.gaussian_process import GaussianProcessRegressor\n",
    "from sklearn.gaussian_process.kernels import ConstantKernel, RBF\n",
    "\n",
    "rbf = ConstantKernel(1.0) * RBF(length_scale=1.0)\n",
    "gpr = GaussianProcessRegressor(kernel=rbf, alpha=noise**2)\n",
    "\n",
    "# Reuse training data from previous 1D example\n",
    "gpr.fit(X_train, Y_train)\n",
    "\n",
    "# Compute posterior mean and covariance\n",
    "mu_s, cov_s = gpr.predict(X, return_cov=True)\n",
    "\n",
    "# Obtain optimized kernel parameters\n",
    "l = gpr.kernel_.k2.get_params()['length_scale']\n",
    "sigma_f = np.sqrt(gpr.kernel_.k1.get_params()['constant_value'])\n",
    "\n",
    "# Compare with previous results\n",
    "assert(np.isclose(l_opt, l))\n",
    "assert(np.isclose(sigma_f_opt, sigma_f))\n",
    "\n",
    "# Plot the results\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GPy\n",
    "\n",
    "[GPy](http://sheffieldml.github.io/GPy/) is a Gaussian processes framework from the Sheffield machine learning group. It provides a `GPRegression` class for implementing GP regression models. By default, `GPRegression` also estimates the noise parameter $\\sigma_y$ from data, so we have to `fix()` this parameter to be able to reproduce the above results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       ".pd{\n",
       "    font-family: \"Courier New\", Courier, monospace !important;\n",
       "    width: 100%;\n",
       "    padding: 3px;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<p class=pd>\n",
       "<b>Model</b>: GP regression<br>\n",
       "<b>Objective</b>: 7.7117630899991365<br>\n",
       "<b>Number of Parameters</b>: 3<br>\n",
       "<b>Number of Optimization Parameters</b>: 2<br>\n",
       "<b>Updates</b>: True<br>\n",
       "</p>\n",
       "<style type=\"text/css\">\n",
       ".tg  {font-family:\"Courier New\", Courier, monospace !important;padding:2px 3px;word-break:normal;border-collapse:collapse;border-spacing:0;border-color:#DCDCDC;margin:0px auto;width:100%;}\n",
       ".tg td{font-family:\"Courier New\", Courier, monospace !important;font-weight:bold;color:#444;background-color:#F7FDFA;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg th{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;color:#fff;background-color:#26ADE4;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:#DCDCDC;}\n",
       ".tg .tg-left{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:left;}\n",
       ".tg .tg-center{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:center;}\n",
       ".tg .tg-right{font-family:\"Courier New\", Courier, monospace !important;font-weight:normal;text-align:right;}\n",
       "</style>\n",
       "<table class=\"tg\"><tr><th><b>  GP_regression.         </b></th><th><b>              value</b></th><th><b>constraints</b></th><th><b>priors</b></th></tr>\n",
       "<tr><td class=tg-left>  rbf.variance           </td><td class=tg-right> 0.5819029022066837</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  rbf.lengthscale        </td><td class=tg-right>  1.190684449776314</td><td class=tg-center>    +ve    </td><td class=tg-center>      </td></tr>\n",
       "<tr><td class=tg-left>  Gaussian_noise.variance</td><td class=tg-right>0.16000000000000003</td><td class=tg-center> +ve fixed </td><td class=tg-center>      </td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<GPy.models.gp_regression.GPRegression at 0x7f9d0937a890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import GPy\n",
    "\n",
    "rbf = GPy.kern.RBF(input_dim=1, variance=1.0, lengthscale=1.0)\n",
    "gpr = GPy.models.GPRegression(X_train, Y_train, rbf)\n",
    "\n",
    "# Fix the noise variance to known value \n",
    "gpr.Gaussian_noise.variance = noise**2\n",
    "gpr.Gaussian_noise.variance.fix()\n",
    "\n",
    "# Run optimization\n",
    "gpr.optimize();\n",
    "\n",
    "# Display optimized parameter values\n",
    "display(gpr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Obtain optimized kernel parameters\n",
    "l = gpr.rbf.lengthscale.values[0]\n",
    "sigma_f = np.sqrt(gpr.rbf.variance.values[0])\n",
    "\n",
    "# Compare with previous results\n",
    "assert(np.isclose(l_opt, l))\n",
    "assert(np.isclose(sigma_f_opt, sigma_f))\n",
    "\n",
    "# Plot the results with the built-in plot function\n",
    "gpr.plot();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although we can reproduce the kernel parameter optimization results, the variances of the predictions are still higher compared to previous results. This is because `GPy` includes noise variance $\\sigma_y^2$ into predictions. This can be easily reproduced using Equation $(9)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_s, cov_s = posterior(X, X_train, Y_train, l=l_opt, sigma_f=sigma_f_opt, sigma_y=noise)\n",
    "\n",
    "# Include noise into predictions using Equation (9).\n",
    "cov_s = cov_s + noise**2 * np.eye(*cov_s.shape)\n",
    "\n",
    "plot_gp(mu_s, cov_s, X, X_train=X_train, Y_train=Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thanks for reading up to here :-) In another article, I'll show how Gaussian processes can be used for black-box optimization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "\\[1\\] Kevin P. Murphy. [Machine Learning, A Probabilistic Perspective](https://mitpress.mit.edu/books/machine-learning-0), Chapters 4, 14 and 15.  \n",
    "\\[2\\] Christopher M. Bishop. [Pattern Recognition and Machine Learning](http://www.springer.com/de/book/9780387310732), Chapter 6.  \n",
    "\\[3\\] Carl Edward Rasmussen and Christopher K. I. Williams. [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/).  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
